A Survey of Replicator Equations

Abstract

This survey of the "state of the art" of replicator dynamics covers recent developments in the theory of the difference and differential equations which describe the evolution of population frequencies under the influence of selection. Mathematical models of this type play a central role in population genetics, ecology, prebiotic evolution and ethology. They introduce a dynamic element into the theory of normal form games and may also be applied to models of learning and economic evolution. The mathematical aspects considered include fixed-point analysis, the notions of permanence and exclusion, the gradient systems obtained by the introduction of certain Riemann metrics, Hopf bifurcations, and relations with game-theoretical concepts.

This research was undertaken as part of the Feasibility Study on the Dynamics of Macrosystems in the System and Decision Sciences Program.